Second Spacex Tanker Study

Update 3-26-21:  this second tanker study looked at refilling the lunar mission Starship in low circular orbit,  where tanker Starship capacities are high,  then topping it off after moving it to the departure orbit,  with more tankers sent directly to that orbit.  That reduced the number of required tankers,  but not by enough to be truly practical.  The strategy explored in the third study (also posted here) turned out to be the most effective one.

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In Ref. 1,  I defined two elliptical orbits from which a Spacex Starship could be sent fully-fueled on a lunar nearside landing mission,  be unrefueled on the moon,  and return to a free entry landing trajectory at Earth.  Payloads sendable to the moon this way are far smaller than payloads deliverable to low circular Earth orbit,  because payload capacity to the higher-energy orbit is reduced,  as well as the inherently-smaller payload capacity for the lunar flight. 

It makes sense to use the elliptical orbit at which Starship payload capacity to that orbit matches the Starship lunar mission capacity.  Some 75 metric tons can be sent to the moon,  with zero return payload,  from an elliptical orbit that has 300 x 7000 km altitudes.  Some 59 tons can be sent to the moon with a 32 ton return payload,  from an orbit that is 300 x 10,000 km altitudes.

Both elliptic orbits have apogee altitudes that penetrate well into the Van Allen radiation belts.  Thus cargoes delivered this way must be radiation-hard,  and any crew or passengers will require effective shelters from serious radiation exposure.  The “base” of the Van Allen radiation belts is considered to be about 1400 km altitude,  outside the South Atlantic Anomaly. 

In Ref. 2,  I determined the deliverable propellant quantities from two potential Spacex tanker configurations:  a dedicated tanker design with extra tankage volume in the forward spaces,  and an ordinary Starship flown fully fueled,  but at zero payload,  so that it arrives with significant unused propellant.  The scope of that study looked at the 300 x 300 km altitude low circular Earth orbit,  and the two possible elliptical lunar mission departure orbits that “sort-of” bound the problem. 

Deliverable tanker “payload” with either configuration was considerable in low circular orbit,  but a lot less when sent directly to either of the two elliptical orbits.  This is because the higher energy orbits require a whole lot more propellant just to be reached.  In all these scenarios,  the dedicated tanker design carries somewhat more deliverable propellant than the ordinary Starship flown at zero payload.

This basic information is summarized in Figure 1 below.  All figures are located at the end of this article.  The two elliptical lunar departure orbits and associated lunar payloads are in the upper part of the figure.  The tanker delivery capacities are shown for both tanker configurations,  at each of the three orbit locations,  in the lower part of the figure.  In each case,  the Starship/Superheavy tanker vehicle is flown directly to the target orbit location,  as is the cargo/passenger Starship/Superheavy vehicle. 

Two Waves Of Refueling On-Orbit

The small tanker propellant delivery capacities to elliptic orbit versus the large capacities to low circular orbit suggested a two-step refueling operation for the lunar-bound Starship:  a full-capacity refill in low circular orbit,  followed by moving it to the elliptic orbit,  with another refill there.  This would apply to either lunar mission scenario. It could be done with either tanker configuration.  Hopefully,  fewer tanker flights would be required than by direct one-step refueling in the elliptic departure orbit.

To support this two-step refueling operation,  I had to figure out what the refill requirements would be upon arrival in the target elliptic orbit,  and also the low circular refueling requirements when carrying the smaller lunar payloads.  The elliptic refill requirements I hand-calculated,  and these are summarized in Figure 2.  The low circular refuel requirements at lower payloads,  I figured with one of the Starship spreadsheet models.  Those results are Figure 3 for the 75 ton payload from the 7000 km apogee orbit,  and in Figure 4 for the 59 ton payload from the 10,000 km apogee orbit.

Calculating Numbers of Tanker Flights

Then I calculated the number of tanker flights required to carry out these operations (first the low circular refill,  then second the elliptic refuel after moving there).  In each operation,  the requisite tankers are flown directly to the orbit where the refill will take place. The limiting number of tanker flights is the refill requirement divided by tanker delivery capacity,  but the only such number that makes any sense is an integer!  You always hold back the tanker landing reserve from deliverable propellant. 

If there are decimals,  you must round up to the next-larger integer!  That is because you cannot carry more deliverable propellant than the max capacities these calculations have identified,  but you can always carry a little less than max capacity. 

Intermediate Results

The refill requirements in low circular orbit for the lunar-bound Starship are just about 1050 tons of propellant,  depending upon which mission and payload we are talking about.  The tanker capacities to low circular orbit are right at 200 tons per vehicle,  give or take,  depending upon whether the tanker is the dedicated design or the ordinary Starship flown as a tanker.  Those numbers and the rounded-up integer numbers of flights are given in Figure 5.  Note that the delivered tanker loads are just not very far from the max capacities of the tankers,  as also given in the figure.   We are looking at 5 dedicated tankers,  or 6 ordinary tankers,  to accomplish this,  for either lunar departure scenario.

The second refueling operation is illustrated in Figure 6.  The refill requirements are far smaller,  but then so are the max tanker capacities!  Again,  you round up the decimals to the next larger integer number of tankers.  Those results show 3 tankers (of either type) are needed for the 300 x 7000 km orbit that supports 75 ton lunar landings,  with 0 tons return payload.  The more demanding 300 x 10,000 km orbit requires 5 tankers of either type,  but that scenario supports a 32 ton return payload,  with 59 tons landed on the moon.  It is the higher-energy orbit.

Ultimate Results

A summary comparison of these results versus the direct staging in elliptical orbit,  and versus operations only to 300 x 300 km circular  are given in Figure 7.  That figure this summarizes the results of the first tanker study and this second one. 

The max payload deliverable to low circular orbit is quite a bit more at 171 metric tons.  That is why 7 ordinary or 6 dedicated tankers are needed to fully refill the Starship there.  That’s a Ref. 2 result.

Another Ref. 2 result is the single refueling operation conducted with Starship and tanker flights directly to the lunar departure elliptic orbit.  That is also indicated in the figure,  which shows some 21 ordinary or 19 dedicated tanker flights to refill the Starship carrying 75 tons to the moon from the 300 x 7000 km orbit.  The Starship carrying 59 tons from the 300 x 10,000 km orbit requires 17 ordinary or 15 dedicated tanker flights to fully refill.  Those high tanker flight numbers are not very attractive!

The two-refill operation approach analyzed in this article (with the first wave of tankers sent to low circular orbit,  and the second wave of tankers sent to the departure elliptic orbit) does indeed reduce the number of tanker flights.  For the 300 x 7000 km departure with 75 tons to the moon,  the first wave is 6 ordinary or 5 dedicated tankers to circular,  followed by the second wave of 3 ordinary or 3 dedicated tankers to the elliptical orbit,  for a total of 9 ordinary or 8 dedicated tankers to support the mission.  For the 300 x 10,000 km departure (59 tons to the moon),  the first wave is the same 6 ordinary or 5 dedicated tankers,  and the second wave is 5 ordinary or 5 dedicated,  for a total of 11 ordinary or 10 dedicated tankers to support that mission.  That is a substantial improvement,  but still unattractive.

Remarks

Readers need to be aware that these calculations I have made are not any sort of simulations run with any sort of computer programs.  These are the kind of calculations I would make,  if I sat down at the kitchen table with pencil,  paper,  and a pocket calculator (or even a slide rule).  These have been semi-automated with spreadsheet software,  but are essentially the same very simple calculations made with simple models,  plus the engineering art of selecting the right “jigger factors” to get realistic results. 

For those readers too young to know what a slide rule is,  see Ref. 3.

Plans

The improvement achieved with two-step refilling is attractive,  and the disparity between tanker capacities in low circular versus feasible lunar departure orbits is large.  That suggests refilling not only the lunar mission Starship in low Earth orbit,  but also 1 or maybe 2 tankers.  The mission Starship plus the 1 or 2 refilled tankers would then move to the elliptical departure orbit,  where those tankers would top-off the mission Starship.  As time and opportunity permits,  I will look at this method of employing these assets,  to see if the total number of supporting tanker flights can be reduced further.

References (all are located on this site)

#1. G. W. Johnson,  Reverse Engineering Estimates:  Starship Lunar Landings,  dated 15 March 2021.

#2. G. W. Johnson,  Spacex Tanker Investigation,  dated 17 March 2021.

#3. G. W. Johnson,  THIS Is a Slide Rule!,  dated 16 March 2019.

Figure 1 – Selected Results From the First Tanker Investigation

Figure 2 – Determining the Refueling Needs Moving From Circular to Elliptical With Lunar Payloads

Figure 3 – Determining the Refueling Needs in Circular with Lunar Payloads:  75 ton

Figure 4 – Determining the Refueling Needs in Circular with Lunar Payloads:  59 ton

Figure5 – Tankers Required to Refuel Lunar-Bound Starships in Circular Orbit (First Refuel)

Figure 6 – Tankers Required to Refuel Lunar-Bound Starships in Elliptical Orbit (Second Refuel)

Figure 7 – Comparison of First Investigation Results with Results of Second Study